Thread: Are equilateral triangles isosceles?

I have noticed that there is no real "convention" about the question of whether isosceles are defined to have 2 equally long sides, or at least 2 equally long sides. Several websites I went to have contradicted each other. Any ideas?

Yes,

if you start with a horizontal line,
then raise the midpoint above it to form an isosceles triangle of any height,
the angles at both ends of the base go from zero to 90 degrees,
as the triangle goes from a horizontal line to a vertical line.
Somewhere between those extremes, the isosceles triangle is also equilateral.

Originally Posted by Archie Meade

Yes,

if you start with a horizontal line,
then raise the midpoint above it to form an isosceles triangle of any height,
the angles at both ends of the base go from zero to 90 degrees,
as the triangle goes from a horizontal line to a vertical line.
Somewhere between those extremes, the isosceles triangle is also equilateral.

Thanks, I wasn't really sure because I saw the "exactly 2 sides of equal length" definition on a relatively reliable website, but I'll go with you and what Wolfram says.